The peculiarity of AD is immediately evident when studying the other social norms. While the anti-defector social norm results in both the greatest population fitness (Fig. SREF ) and increase in cooperation, all other social norms are unable to sustain levels of cooperation higher than the baseline, resulting in populations largely dominated by loners (Fig. REF ) with a cyclical pattern similar to those of [1]}. The reason for this divergence lays in the reputational damage inflicted by these norms to non-cooperators. Indeed while reputation helps agents condition their behaviour to opponents' types, attributing loners a bad reputation does not inflict on them any direct damage. Since they are already prone to not participating in the game, their payoffs remain independent from any reputational effect. However, attributing loners too low a reputation (in AL and AB) hampers the role of loners in providing a backup option against invading defectors. Furthermore, not attributing defectors a strictly lower reputation (in AN), allows them to more easily exploit cooperators by impeding the latter to discriminate between loners and defectors (the full transition matrices are reported in SM Figs. SREF  - SREF ). In all these cases the effectiveness of C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  against defection is more limited hence the strategy has limited evolutionary success (Fig. REF , panels B, C, D and SM Fig. SREF ). For this reason, in the following we will focus our attention mainly on the AD social norm.
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